In this section, we introduce the Entropic Risk Thompson Sampling (ERTS) algorithm for Gaussian bandits with bounded variances, i.e., \(\nu \in E_{N}^K(\sigma _{\max }^2) := \lbrace \nu =(\nu _1,\dots ,\nu _K) : \nu _i \sim N(\mu _i,\sigma _i^2), \sigma _i^2 \le \sigma _{\max }^2\ \forall i \in [K]\rbrace \)  for some \(\sigma _{\max }^2 > 1\) . Similar to [1]} and [2]}, the algorithm samples from the posteriors of each arm, then chooses the arm according to a multi-criterion procedure.
